On non-equilibrium dynamics of multidimensional infinite particle systems in the translation invariant case

It is shown that for a set of full measure with respect to any translation invariant probability distribution on the space of initial configurarations of classical particle systems on ^d with interaction given by a smooth superstable potential of finite range there is a solution to the Newtonian equations of motion, provided that the specific energy and the particle density of the initial configuration exist a.s.